WORK 1 successive infinitesimal displacements. Therefore the wo done in any displacement is given by the integral W = I F cos a ds. i = P Jo' When the path of the particle is curved the direction of coincides with that of the tangent to the curve. Therefc F cos a is the tangential component of the force. In ott words the tangential component of force does all the wo] Hence W= f*FTds. _( */ The normal component does no work because the par|ii is not displaced along it. — Special Cases. Case I.—When the force is constant, jbo in direction and in magnitude, it can be taken out of-t integrand. Therefore W = F I cos a ds. <- Jo The last integral equals the projection of the path upon t direction of the force. Therefore the product of the foi by the projection of the path upon the line of action of t force equals the work done. Case II. — When the force is constant and the path straight then the angle between the force and the displa< ment is constant. Therefore W = F cos a I ds Jo = Fs cos a. Case III.—When the force is not only constant but also parallel to the path, then a = 0. Therefore W = Fs. Case IV. —When the force is at right angles to the d placement a = ^, and cos a = 0. Hence W = 0. Therefc 2 the force does no work unless it has a component along t